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Inverse Proportionality

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by Priyaranjan » Thu Nov 26, 2015 9:23 pm
Q. The "luminous flux", or perceived brightness, of a light source is measured in lumens and is inversely proportional to the square of the distance from the light. If a light source produces 200 lumens at a distance of 3 meters, at what distance will the light source produce a luminous flux of 25 lumens?
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by Matt@VeritasPrep » Thu Nov 26, 2015 11:37 pm
Inverse proportion says

x * y = some constant, for the two variables x and y. (We don't need to know what this constant is, as we'll see below; we just need to know that it doesn't change.)

In our case, x = lumens and y² = distance.

In the first case, x = 200 and y = 3.

In the second case, x = 25, and y = unknown.

Since they have to equal the same constant, given that they have the same inverse ratio, our equation is

200 * 3² = 25 * (distance we want)²

This gives

(Distance we want)² = 72, or

Distance we want = √72 = 6√2
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